Why does increasing resolution and then downsampling to desired size increase render quality?
If you render at 256x256, each pixel gets only 16 samples of AA.

If you increase the resolution to 1080x1080, the same area is now covered with 16 pixels (4x4). So the area now get's 16 times more AA samples.

By rendering larger you get also less noise in the image on the Ambient Occlusion and that also helps with the clarity when sampled down to small size.